Optical filters, which are filters used to filter electromagnetic radiation in the ultraviolet/visible/infrared portions of the electromagnetic spectrum, are used in a multitude of applications, and typically consist of continuous thin films that are deposited on a substrate. FIG. 1 shows an optical filter 10, which comprises a thin film 12 that has been deposited on substrate 18.
The intensity of light in a non-conductive media at thickness z, shown in FIG. 1, is given byI=I0e^(−αz)
where I is the intensity at depth z, I0 is the intensity at a reference thickness, and α is the absorption coefficient of the material.
The transmission, or transmissivity, T, of a thin film as a function of thickness z and wavelength λ and is defined asT(z,λ)≡I(z,λ)/I0 
It can thus be shown thatT(z,λ)=T0^(z/z0)  (1)
where To is a reference transmission of the film at thickness z0 for any thin film.
FIG. 2 shows example transmission curves for a continuous thin film as a function of thin film thickness in the z direction, the same direction as the incident light. As the thickness of a given thin film material increases, the transmission of light through it generally decreases for a given wavelength.
FIG. 3 illustrates a thin-film stack 20, consisting of multiple layers 22, 24, and 26 deposited on substrate 28 made of suitable optical material.
The above equation (1) can be generalized for n layers. For n=3 thin films, a, b, and c,T(z,λ)=Ta0^(za/za0)*Tb0^(zb/zb0)*Tc0^(zc/zc0)  (2)
where Ta0, Tb0, and Tc0 are the respective reference transmissions of films of thickness za0, zb0 and zc0, respectively. This expression can be generalized to provide the total transmission of any stack of n thin film layers.
FIG. 4 shows an exemplary experimentally measured two-layer filter transmission spectrum, as well as the experimentally measured spectra of the individual continuous film layers C1 and C2 making up the two-layer filter. Note that the two-layer spectrum, shown in a dark solid line, may alternately be determined by multiplying the individual coating layer transmissions at a given wavelength.
In designing useful products, product designers typically design optical filters by defining a target transmission spectrum for the particular application, and then send their specifications to thin film filter specialists to manufacture, through a lengthy trial and error process, a film, or combination of films that will produce a transmission spectrum that resembles the one specified. This process is highly iterative with the design cycle taking weeks, months, or even years to satisfactorily match a given target transmission spectrum for an optical filter.
Conventional techniques for fabricating thin-film optical filters include, for example, vacuum vapor deposition, deposition by electron-beam evaporation (EBE), techniques based on ion-assisted deposition (IAD), reactive ion plating, and ion-beam sputtering. All techniques utilize similar well-established batch manufacturing sequences that are slow, expensive, and only accommodate the production of optical filters whose size or “footprint” is on the order of centimeters across. Additionally, because the control of thin film filter layer thickness is often difficult to precisely control, it can difficult, if not impossible, to manufacture thin film filters that closely match predefined transmission spectra.